No, it is not wrong.

If nobody used animals to make a living then we would not have meat, cheeses, eggs, drug sniffing dogs, bomb detecting dogs (yes there is such a thing), or anything like that. There wouldn't even be pets, after all the breeders of pets are making a living off of the animals they breed and sell. Animals are used as food, companions, and even law enforcement heroes. Imagine a world where nobody used animals. I know my life isn't complete without my four legged companions.

How would it be wrong?

This will catch tons of flak from animal rights people, but explain how animals have the same rights as humans before you start whining. First off, people milk cows and goats, and sell the milk, cheese, and butter that those animals make. It doesn't harm the cow in the least. Second, many people survive by killing/ using animal products. Butchers, farmers, ranchers, and cowboys all use animals for a living. Even professional fisherman need fish to make money, technically. Most of their income comes from sponsors and prize money. Third, while the animal feels some pain in their death in the slaughter house, or during their capture for a bass tournament, that pain is temporary, and slaughter houses are becoming more humane as time passes. Fourth, what ethical problem is there with using God's gift of dominion over animals? Because your religion, or lack thereof, says that animals are better? If animals are indeed better than man, why do we control them?